Details

sample151.0ms

Algorithm

intervals

Results

69.0ms	96×	body	1280	valid
29.0ms	62×	body	640	valid
28.0ms	17×	body	2560	valid
9.0ms	35×	body	320	valid
3.0ms	34×	body	80	valid
2.0ms	12×	body	160	valid

simplify5.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	9	4
1	10	4
2	10	4

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 38.0b

localize8.0ms

Local error

Found 2 expressions with local error:

2.1b	(- (tan (+ x eps)) (tan x))
2.6b	(tan (+ x eps))

rewrite23.0ms

Algorithm

rewrite-expression-head

Rules

4×	`tan-quot` `add-sqr-sqrt` `*-un-lft-identity` `add-log-exp`
2×	`pow1` `add-exp-log` `add-cube-cbrt` `tan-sum` `frac-sub` `add-cbrt-cube`
1×	`sub-neg` `flip3--` `diff-log` `flip--` `distribute-lft-out--` `difference-of-squares`

Counts

2 → 25

Calls

2 calls:

16.0ms	(- (tan (+ x eps)) (tan x))
6.0ms	(tan (+ x eps))

series131.0ms

Counts

2 → 6

Calls

2 calls:

81.0ms	(- (tan (+ x eps)) (tan x))
50.0ms	(tan (+ x eps))

simplify80.0ms

Algorithm

egg-herbie

Counts

31 → 31

Iterations

Useful iterations: 3 (23.0ms)

Iter	Nodes	Cost
0	134	211
1	295	202
2	757	200
3	2482	199
4	5001	199

prune87.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 14.4b

localize11.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps))))
0.1b	(+ (tan x) (tan eps))
0.2b	(* (tan x) (tan eps))
4.5b	(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))

rewrite133.0ms

Algorithm

rewrite-expression-head

Rules

27×	`*-un-lft-identity`
22×	`add-sqr-sqrt`
15×	`add-cube-cbrt`
13×	`times-frac`
9×	`tan-quot`
8×	`add-exp-log` `add-cbrt-cube` `add-log-exp`
6×	`pow1`
5×	`distribute-lft-out`
4×	`associate-/l*`
3×	`associate-r` `associate-l` `associate-/r*` `associate-/l/`
2×	`flip3--` `flip3-+` `frac-add` `associate-/r/` `flip--` `flip-+` `difference-of-squares`
1×	`cbrt-undiv` `+-commutative` `frac-times` `sub-neg` `frac-2neg` `diff-log` `associate-r/` `div-exp` `pow-prod-down` `associate-l/` `prod-exp` `clear-num` `sum-log` `*-commutative` `frac-sub` `cbrt-unprod` `div-inv` `distribute-lft-out--` `unswap-sqr`

Counts

4 → 86

Calls

4 calls:

28.0ms	(/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps))))
8.0ms	(+ (tan x) (tan eps))
15.0ms	(* (tan x) (tan eps))
78.0ms	(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))

series685.0ms

Counts

4 → 12

Calls

4 calls:

195.0ms	(/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps))))
81.0ms	(+ (tan x) (tan eps))
83.0ms	(* (tan x) (tan eps))
326.0ms	(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))

simplify49.0ms

Algorithm

egg-herbie

Counts

98 → 98

Iterations

Useful iterations: 2 (39.0ms)

Iter	Nodes	Cost
0	397	1050
1	1432	1005
2	5001	995

prune278.0ms

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 14.3b

localize21.0ms

Local error

Found 4 expressions with local error:

0.1b	(+ (tan x) (tan eps))
0.2b	(* (sin x) (sin eps))
0.2b	(/ (* (sin x) (sin eps)) (* (cos eps) (cos x)))
4.5b	(- (/ (+ (tan x) (tan eps)) (- 1 (/ (* (sin x) (sin eps)) (* (cos eps) (cos x))))) (tan x))

rewrite275.0ms

Algorithm

rewrite-expression-head

Rules

18×	`add-exp-log` `add-cbrt-cube`
13×	`add-sqr-sqrt`
10×	`*-un-lft-identity`
8×	`add-log-exp`
6×	`pow1` `add-cube-cbrt`
5×	`prod-exp` `cbrt-unprod`
4×	`cbrt-undiv` `div-exp`
3×	`tan-quot` `associate-r` `associate-l`
2×	`times-frac` `sin-mult` `difference-of-squares`
1×	`+-commutative` `sub-neg` `flip3--` `frac-2neg` `flip3-+` `diff-log` `pow-prod-down` `frac-add` `clear-num` `associate-/r` `sum-log` `associate-/r/` `cos-mult` `-commutative` `frac-sub` `flip--` `flip-+` `div-inv` `associate-/l/` `distribute-lft-out` `associate-/l*` `distribute-lft-out--` `unswap-sqr`

Counts

4 → 71

Calls

4 calls:

8.0ms	(+ (tan x) (tan eps))
12.0ms	(* (sin x) (sin eps))
18.0ms	(/ (* (sin x) (sin eps)) (* (cos eps) (cos x)))
236.0ms	(- (/ (+ (tan x) (tan eps)) (- 1 (/ (* (sin x) (sin eps)) (* (cos eps) (cos x))))) (tan x))

series571.0ms

Counts

4 → 12

Calls

4 calls:

88.0ms	(+ (tan x) (tan eps))
45.0ms	(* (sin x) (sin eps))
98.0ms	(/ (* (sin x) (sin eps)) (* (cos eps) (cos x)))
341.0ms	(- (/ (+ (tan x) (tan eps)) (- 1 (/ (* (sin x) (sin eps)) (* (cos eps) (cos x))))) (tan x))

simplify51.0ms

Algorithm

egg-herbie

Counts

83 → 83

Iterations

Useful iterations: 1 (12.0ms)

Iter	Nodes	Cost
0	437	917
1	1799	792
2	5001	792

prune326.0ms

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 14.3b

localize12.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (tan x) (tan eps))
0.2b	(/ (- 1 (* (tan x) (tan eps))) (+ (tan x) (tan eps)))
0.3b	(/ 1 (/ (- 1 (* (tan x) (tan eps))) (+ (tan x) (tan eps))))
7.4b	(- (/ 1 (/ (- 1 (* (tan x) (tan eps))) (+ (tan x) (tan eps)))) (tan x))

rewrite199.0ms

Algorithm

rewrite-expression-head

Rules

123×	`times-frac`
104×	`*-un-lft-identity`
83×	`add-sqr-sqrt`
67×	`add-cube-cbrt`
23×	`associate-/r*`
19×	`add-exp-log`
16×	`associate-/r/` `distribute-lft-out`
15×	`tan-quot`
13×	`add-cbrt-cube`
8×	`div-exp`
7×	`pow1` `div-inv`
6×	`associate-/l*` `add-log-exp`
5×	`flip3-+` `frac-add` `flip-+` `difference-of-squares`
4×	`cbrt-undiv`
3×	`associate-r` `associate-l`
2×	`rec-exp` `flip3--` `frac-2neg` `1-exp` `clear-num` `flip--` `associate-/l/` `distribute-lft-out--`
1×	`frac-times` `sub-neg` `pow-flip` `diff-log` `div-sub` `associate-r/` `pow-prod-down` `associate-l/` `prod-exp` `*-commutative` `frac-sub` `cbrt-unprod` `inv-pow` `unswap-sqr`

Counts

4 → 178

Calls

4 calls:

16.0ms	(* (tan x) (tan eps))
22.0ms	(/ (- 1 (* (tan x) (tan eps))) (+ (tan x) (tan eps)))
25.0ms	(/ 1 (/ (- 1 (* (tan x) (tan eps))) (+ (tan x) (tan eps))))
130.0ms	(- (/ 1 (/ (- 1 (* (tan x) (tan eps))) (+ (tan x) (tan eps)))) (tan x))

series821.0ms

Counts

4 → 12

Calls

4 calls:

82.0ms	(* (tan x) (tan eps))
234.0ms	(/ (- 1 (* (tan x) (tan eps))) (+ (tan x) (tan eps)))
192.0ms	(/ 1 (/ (- 1 (* (tan x) (tan eps))) (+ (tan x) (tan eps))))
314.0ms	(- (/ 1 (/ (- 1 (* (tan x) (tan eps))) (+ (tan x) (tan eps)))) (tan x))

simplify86.0ms

Algorithm

egg-herbie

Counts

190 → 190

Iterations

Useful iterations: 2 (59.0ms)

Iter	Nodes	Cost
0	703	2793
1	3294	2509
2	5001	2506

prune368.0ms

Pruning

18 alts after pruning (18 fresh and 0 done)

Merged error: 14.2b

regimes177.0ms

Accuracy

89.2% (0.8b remaining)

Error of 15.1b against oracle of 14.3b and baseline of 21.8b

bsearch170.0ms

Steps

Iters	Range		Point
9	4.9236548997223346e-36	6.481252319714892e-31	1.9383709758799288e-31
9	-2.2082264187638084e-10	-1.8774124276059505e-19	-9.832752395103018e-18

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	35	22
1	35	22

end0.0ms

sample4.9s

Algorithm

intervals

Results

2.4s	3249×	body	1280	valid
1.1s	660×	body	2560	valid
761.0ms	1872×	body	640	valid
212.0ms	764×	body	320	valid
91.0ms	1126×	body	80	valid
58.0ms	329×	body	160	valid